Finite volume chiral partition functions and the replica method

In the framework of chiral perturbation theory we demonstrate the equivalence of the supersymmetric and the replica methods in the symmetry breaking classes of Dyson indices [Formula Presented] and [Formula Presented] Schwinger-Dyson equations are used to derive a universal differential equation for the finite volume partition function in sectors of fixed topological charge, [Formula Presented] All dependence on the symmetry breaking class enters through the Dyson index [Formula Presented] We utilize this differential equation to obtain Virasoro constraints in the small mass expansion for all [Formula Presented] and in the large mass expansion for [Formula Presented] with arbitrary [Formula Presented] Using quenched chiral perturbation theory we calculate the first finite volume correction to the chiral condensate demonstrating how, for all [Formula Presented] there exists a region in which the two expansion schemes of quenched finite volume chiral perturbation theory overlap. © 2003 The American Physical Society.